Related papers: Note on Euler characteristic of a toric vector bun…

Characterizations of all continuous, additive and $\mathrm{GL}(n)$-equivariant endomorphisms of the space of convex functions on a Euclidean space $\mathbb{R}^n$, of the subspace of convex functions that are finite in a neighborhood of the…

The Losev-Manin moduli space parametrizes pointed chains of projective lines. In this paper we study a possible generalization to families of pointed degenerate toric varieties. Geometric properties of these families, such as flatness and…

Motivated by representation theory and geometry, we introduce and develop an equivariant generalization of Ehrhart theory, the study of lattice points in dilations of lattice polytopes. We prove representation-theoretic analogues of…

Let G be a countable discrete group and let M be a smooth proper cocompact G-manifold without boundary. The Euler operator defines via Kasparov theory an element, called the equivariant Euler class, in the equivariant K-homology of M. The…

Equivariant Ehrhart theory enumerates the lattice points in a polytope with respect to a group action. Answering a question of Stapledon, we describe the equivariant Ehrhart theory of the permutahedron, and we prove his Effectiveness…

Euler-symmetric projective varieties are nondegenerate projective varieties admitting many C*-actions of Euler type. They are quasi-homogeneous and uniquely determined by their fundamental forms at a general point. We show that…

We determine all the equivariant Euler characteristics of the building for the general unitary group over a finite field.

Using a covariant description of the geometry of deformations for extendons, it is shown that the topological corrections for the string action associated with the Euler characteristic and the first Chern number of the normal bundle of the…

A theorem due to D. Bernstein states that Euler characteristic of a hypersurface defined by a polynomial f in (C\{0})^n is equal (upto a sign) to n! times volume of the Newton polyhedron of f. This result is related to algebaric torus…

We provide two new characterizations of bounded orthogonally additive polynomials from a uniformly complete vector lattice into a convex bornological space using separately two polynomial identities of Kusraeva involving the root mean power…

Morelli's computation of the K-theory of a toric variety X associates a polyhedrally constructible function on a real vector space to every equivariant vector bundle E on X. The coherent-constructible correspondence lifts Morelli's…

A geometric interpretation of curvature and torsion of linear transports along paths is presented. A number of (Bianchi type) identities satisfied by these quantities are derived. The obtained results contain as special cases the…

The notion of the orbifold Euler characteristic came from physics at the end of 80's. There were defined higher order versions of the orbifold Euler characteristic and generalized ("motivic") versions of them. In a previous paper the…

For any two nef line bundles F and G on a toric variety X represented by lattice polyhedra P respectively Q, we present the universal equivariant extension of G by F under use of the connected components of the set theoretic difference of Q…

We present a geometric interpretation of tight closure in terms of vector bundles and projective bundles.

In this paper, we define an action of the group of equivariant Cartier divisors on a toric variety X on the equivariant cycle groups of X, arising naturally from a choice of complement map on the underlying lattice. If X is nonsingular,…

We demonstrate that the generalization of the relativistic Toda chain (RTC) is a special reduction of two-dimensional Toda Lattice hierarchy (2DTL). This reduction implies that the RTC is gauge equivalent to the discrete AKNS hierarchy and,…

Datasets are mathematical objects (e.g., point clouds, matrices, graphs, images, fields/functions) that have shape. This shape encodes important knowledge about the system under study. Topology is an area of mathematics that provides…

A vector bundle $E$ over a projective variety $M$ is called finite if it satisfies a nontrivial polynomial equation with nonnegative integral coefficients. Introducing finite bundles, Nori proved that $E$ is finite if and only if the…

We construct the categories of standard vector bundles over schemes and define direct sum and tensor product. These categories are equivalent to the usual categories of vector bundles with additional properties. The tensor product is…